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    翟文广


    翟文广

    民族: 汉  性别:男    教授,博士生导师 

    Email: zhaiwg@hotmail.com wgzhai@163.com

    一、教育背景 

      (1) 1987.09—1991.07,山东大学数学系,理学学士 

      (2) 1991.09—1996.07,山东大学数学系,理学博士(硕博连读) 

      (3)2001.10—2003.09,日本名古屋大学多元数理科学研究科,博士后

    二、工作经历 

       (1) 1996.07—1997.11,山东师范大学数学系,讲师 

       (2)1997.12—1999.11,山东师范大学数学系,副教授 

       (3)1999.12--2010.07,山东师范大学数学科学学院,教授

       (4)2001.10-2003.9, 日本名古屋大学(多元数理),博士后。 

       (5)2010.08-至今,中国矿业大学(北京)澳门大阳城娱乐登录,教授

    三、学术兼职 

      (1)2001.03至今,《数学评论》评论员 

      (2)2005.05至今, 西北大学博士生导师 

      (3)2010.01至今,《纯粹数学与应用数学》编委 

      (4)2015.01至今,《数学进展》编委

    四、学术研究 

        1研究方向:解析数论 

        2. 研究项目   

        (1).主持科研项目

    · [1]1999.01—2001.12,山东省自然科学基金:指数和估计与整点问题(编号:Q98A02110

    · [2]2004.01—2006.12, 国家自然科学基金:多维指数和估计与离散Hardy-Littlewood方法(项目编号:10301018) 

    · [3]2005.01—2005.12, 国家留学基金委留学回国人员项目:平面原整点问题

    · [4]2006.01—2008.12, 山东省自然科学基金:平面原整点问题(编号:Y2006A31) 

    · [5]2008.01—2010.12,国家自然科学基金:解析数论中若干重要余项的积分均值(项目编号:10771127)

    · [6]2012.01—2015.12, 国家自然科学基金:一般除数问题的若干问题(项目编号:11171344) 

    · [7]2020.01—2023.12, 国家自然科学基金:解析数论的若干问题(项目编号11971476)

           (2).参加科研项目 

    · [1]1998.01—2000.12, 山东省自然科学基金:三角和估计及其应用

    · [2]1999.01—2001.12,国家自然科学基金:素变数丢番图逼近(项目编号:19801021)

    · [3]2009.01—2009.12,国家自然科学基金委天元基金:自守L函数与零点密度估计(编号:10826028) 

    · [4]2011.01—2013.12, 北京市自然科学基金项目:非对称除数问题(编号:1112010) 

         (3)、部分学术论文   

    · [1] On the distribution of {x/n}. II, Chinese Sci. Bull. 41 (1996), no. 1, 1-5 

    · [2] On a multiplicative hybrid problem, Acta Arith. 71 (1995), no. 1, 47--53 

    · [3]Reciprocal sums of a class of additive functions in short intervals, Chinese Sci. Bull. 42 (1997), no. 2, 102—105 

    · [4](with Xiaodong Cao)On the average number of direct factors of finite abelian groups, Acta Arith. 82 (1997), no. 1, 45--55

    · [5] A note on a result of Abercrombie, Chinese Sci. Bull. 42 (1997), no. 14, 1151--1154

    · [6](with Xiaodong Cao) On the number of coprime integer pairs within a circle, Acta Arith. 90 (1999), no. 1, 1--16

    · [7] On the average number of direct factors of finite abelian groups. II, Acta Arith. 90 (1999), no. 1, 69--78

    · [8] The additive completion of k-th powers, J. Number Theory 79 (1999), no. 2, 292—300 

    · [9] On sums and differences of two coprime k-th powers, Acta Arith. 91 (1999), no. 3, 233--248

    · [10]On the k-dimensional Piatetski-Shapiro prime number theorem, Sci. China Ser. A 42 (1999), no. 11, 1173--1183

    · [11]On a system of two Diophantine inequalities with prime numbers, Acta Arith. 92 (2000), no. 1, 31--46 

    · [12](with Xiaodong Cao)] Multiple exponential sums with monomials, Acta Arith. 92 (2000), no. 3, 195—213

    · [13](with Xiaodong Cao) On the distribution of r-full and l-free integers in short intervals, Monatsh. Math. 130 (2000), no. 1, 71—84 

    · [14] On the average number of unitary factors of finite abelian groups. II, Acta Math. Sin. (Engl. Ser.) 16 (2000), no. 4, 549--554 

    · [15]  On Three-Dimensional Divisor Problem of (a,a,b) type. Adv. Math. (China) 29 (2), 137–146, 2000.

    · [16] Number of B-free numbers in short intervals. Chinese Sci. Bull., 45 (3), 208–212, 2000. 

    · [17] On the simultaneous distribution of the fractional parts of different powers of prime numbers, J. Number Theory 86 (2001), no. 1, 133--155

    · [18](with Guangshi Lü) A Special Divisor Problem, Acta Math. Sinica (Chin. Ser.) 45 ( 5), 991–1004, 2002.

    · [19] On the Number of Primitive Pythagorean Triangles, Acta Arith. 105 (4), 387–403, 2002.

    · [20](with Xiaodong Cao) A Diophantine Inequality with Prime Numbers,  Acta Math. Sinica (Chin. Ser.), 45(2),  361–370, 2002.

    · [21](with Xiaodong Cao) On Systems of Diophantine Inequalities and Equations with Prime Numbers, Adv. Math. (China), 31(3), 243–248, 2002.

    · [22](with Xiaodong Cao) A Diophantine Equation with Prime Numbers, Acta Math. Sinica (Chin. Ser.) 45(3), 443–454, 2002. 

    · [23] (with Xiaodong Cao) On a Binary Diophantine Inequality, Adv. Math. (China), 32(6), 706–721, 2003.

    · [24](with Guangshi Lü) The Sum of Multi-Dimensional Divisor Functions on a Special Sequence, Adv. Math. (China), 32 (6), 660–664, 2003.

    · [25] Short Interval Results for a Class of integers, Monatsh. Math. 140 (3), 233–257, 2003.  

    · [26](with Xiaodong Cao) On a Diophantine Inequality over Primes, Adv. Math. (China), 32(1), 63–73, 2003. 

    · [27] On Primitive Lattice Points in Planar Domains, Acta Arith., 109 (1), 1–26, 2003. 

    · [28](with Guangshi Lü) The Divisor Problem for the Beatty Sequences, Acta Math. Sinica (Chin. Ser.), 47 (6), 1213–1216, 2004. 

    · [29] On Higher-Power Moments of E(t), Acta Arith., 115 (4), 329–348, 2004. 

    · [30](with Guangshi Lü) On Three-Dimensional Divisor Problem of (a,a,b) type, Adv. Math. (China), 33(2), 195–202, 2004.

    · [31] On Higher-Power Moments of Δ(x)(II), Acta Arith. 114(1), 35–54, 2004. 

    · [32] On Higher-Power Moments of Δ(x), Acta Arith. 112 (4), 367–395, 2004.  

    · [33](with Deyu Zhang)  The Waring-Goldbach Problem in Thin Sets of Primes(II), Acta Math. Sinica (Chin. Ser.) 48 (4), 809–816, 2005.

    · [34] On Higher-Power Moments of Δ(x)(III), Acta Arith., 118 (3), 263–281, 2005. 

    · [35] On Sums of Two Coprime k-th powers, Monatsh. Math., 144 (3), 233–250, 2005.  

    · [36](with Deyu Zhang) Differences of Two Relatively Prime Cubes, Acta Math. Sinica (Chin. Ser.) 49(5), 1181–1188, 2006. 

    · [37] On the Mean Value of the Index of Composition of an Integer, Acta Arith, 125 (4), 331–345, 2006.  

    · [38](with Furuya Jun) On the k-Free Divisor Problem, Acta Arith. 123 (3), 267–287, 2006.  

    · [39](with Deyu Zhang,) On Integers n Coprime to , Acta Math. Sinica (Chin. Ser.), 49(2), 469–472, 2006.

    · [40] On Higher-Power Moments of Δ(x) (IV), Acta Math. Sinica (Chin. Ser.), 49 (3), 639–646, 2006.

    · [41](with Deyu Zhang) Estimates of Maximal Divisor of k-th Power, (Chinese) Acta Math. Sinica (Chin. Ser.) 49(1), 205–214, 2006.

    · [42](with  Xiaodong Cao) On Sums of Two Coprime k-th Powers, II. Monatsh. Math. 148(2), 153–172, 2006.  

    · [43] Square-free Integers as Sums of Two Squares, Number theory, 15, 219–227, 2006.  

    · [44](with Xiaodong Cao), On a Diophantine Inequality over Primes, II. Monatsh. Math. 150 (2), 173–179, 2007. 

    · [45] Rényi's Problem in Short Intervals, Acta Math. Sin. (Engl. Ser.) 23(1), 29–36, 2007.  

    · [46](with Tanigawa Yoshio) Dirichlet Series Associated with Polynomials and Applications, J. Number Theory, 122(2), 466–518 ,2007.

    · [47](with Xiaodong Cao) Distribution of Square-Free Numbers of the Form . II, Acta Math. Sinica (Chin. Ser.)., 51(6), 1187–1194, 2008. 

    · [48](with Furuya Jun)  On the k-Free Divisor Problem. II. Acta Arith. 132 (4), 351–358, 2008. 

    · [49](with Tanigawa Yoshio) On the Gcd-Sum Function, J. Integer Seq. 11(2), Article 08.2.3, 2008.

    · [50](with Tanigawa Yoshio and Deyu Zhang) On the Rankin-Selberg Problem: Higher Power Moments of the Riesz Mean Error Term, Sci. China Ser. 51 (1), 148–160, 2008.  

    · [51]On the error term in Weyl’s law for Heisenberg manifolds, Acta Arithmetica,134(2008), 219-257.

    · [52](with LingLing Dong)  On the Distribution of , Acta Math. Sinica (Chin. Ser.), 52(3), 569–578, 2009. 

    · [53]  On the Prime Power Factorization of n!, J. Number Theory, 129(8), 1820–1836, 2009. 

    · [54] On the Error Term in Weyl's Law for the Heisenberg Manifolds. II, Sci. China Ser. A, 52(5), 857–874, 2009.  

    · [55](with Huaning Liu) A Note on the Pseudorandomness of the Liouville Function, Acta Arith., 136(2), 101–121, 2009.  

    · [56](with Guangshi Lü) On the Representation of Large Integers as Sums of Four Almost Equal Squares of Primes, Ramanujan J., 18(1), 1–10, 2009.  

    · [57](with Yoshio Tanigawa) On the Fourth Power Moment of Δ(x) and E(x) in Short Intervals, Int. J. Number Theory, 5(2), 355–382, 2009. 

    · [58](with Xiaodong Cao) On the mean square of the error term for the asymmetric two-dimensional divisor problem, Monatsh Math.159 (2010), no. 1-2,185-209. 

    · [59](with Xiaodong Cao), On the mean square of the error term for the asymmetric two-dimensional divisor problems, Monatsh Math.160 (2010),  no. 4,115-142

    · [60](with Jun Furuya, Yoshio Tanigawa), Dirichlet series obtained from the error term in the Dirichlet divisor problem, Monatsh Math.160 (2010), no. 4,385-402 

    · [61](with Xiaodong Cao, Yoshio Tanigawa), On a conjecture of Chowla and Walum,Scin.China Math.53 (2010), no.2755-2771

    · [62](with Deyu Zhang) On the fifth-power moment of Δ(x) , Int. J of Number Theory, Vol. 7(2011), 71-86

    · [63](with Deyu Zhang) On the mean value of the index of composition of an integral ideal, Journal of Number  Theory 131 (2011), 618–633.

    · [64](with Ivic Aleksandar) On the Dirichlet divisor problem in short intervals. Ramanujan J. 33 (2014), no. 3, 447–465.

    · [65](with Cao, Xiaodong; Furuya, Jun; Tanigawa, Yoshio) On the differences between two kinds of mean value formulas of number-theoretic error terms. Int. J. Number Theory 10 (2014), no. 5, 1143–1170

    · [66]( withGuangshiLü and Jie Wu) On a Divisor Problem Related to the Epstein Zeta-Function (II),J. Number Theory, 131(9), 1734–1742, 2011

    · [67](withI.Kiuchi and Yoshio Tanigawa), Analytic Properties of Double Zeta-functions, Indag. Math., 21(1-2), 16–29, 2011.

    · [68](withRutingGuo),Some problems about the ternary quadratic formm1^2+ m2^2+ m3^2, ActaArithmetica, 156(2), 101-121, 2012

    · .[69](withXiaodong Cao, Jun Furuya and Yoshio Tanigawa), A generalized divisor problem and the sum of Chowla and Walum, JMAA, Vol. 400(2013), 15-21.

    · [70](withDeyu Zhang andMeimeiLv),On the mean value of the index of composition of an integer II, IJNT, Vol.9(2013), 431-445.

    · [71](withAleksandarIvic),Higher moments of the error term in the divisor problem,Mathematical Notes, 88(3-4), 338-346,2010. 

    · [72](withXiaodong Cao), On the Mean Square of the Error Term for the Asymmetric Two-dimensional Divisor Problem(I),Monatsh. Math.,159(1-2), 185–209, 2010

    · [73]( with Kai-Man Tsang), Sign changes of the error term in Weyl’s law for Heisenberg manifolds, Transaction of AMS., 364(5), 2647-2666, 2012

    · [74](with Deyu Zhang) On the Mean Value of the Index of Composition of an Integral Ideal(II), J. Number Theory, 133, 1086–1110, 2013

    · [75](with Jie Wu)  Distribution of Hecke Eigenvalues of newforms in short intervals, Q.J. Math., 64, 619-644, 2013

    · [76](with Aleksandar Ivic) On the Dirichlet divisor problem in short intervals, Ramanujan J (2014) 33:447–465

    · [77] (with Caoxiaodong) On the four-dimensional divisor problem of (a,b,c,c) type, Functiones et Approximatio 49.2 (2013), 251–267

    · [78] (with X. Cao, J. Furuya, Y. Tanigawa ) A generalized divisor problem and the sum of Chowla and Walum II, Functiones et Approximatio 49.1 (2013), 159–188

    · [79] (with X. Cao, J. Furuya, Y. Tanigawa ) On the differences between two kinds of mean value formulas of number-theoretic error terms, International Journal of Number Theory Vol. 10, No. 5 (2014) 1143–1170

    · [80] Asymptotics for a class of arithmetic functions, Acta Arithmetica, 170(2015), 135-160

    · [81](with A. Ivic)  On some mean value results for the zeta-function and a divisor problem II, Indagationes Mathematicae 26 (2015) 842–866

    · [82](with X. Cao and Y. Tanigawa) Mean square of the error term in the asymmetric multidimensional divisor problem, Functiones et Approximatio 54.2 (2016), 173–193 

    · [83] (with X. Cao and Y. Tanigawa) CONTINUED FRACTION EXPRESSION OF THE MATHIEU SERIES, Mathematical Inequalities& Applications, 19(2016) ,1039–1048

    · [84] (with X. Cao and Y. Tanigawa) ON THE MEAN OF THE SHIFTED ERROR TERM IN THE THEORY OF THE DIRICHLET DIVISOR PROBLEM, ROCKY MOUNTAIN JOURNAL OF MATHEMATICS Volume 46, Number 1, 2016,105-124.

    · [85] (with X. Cao and Y. Tanigawa) On the mean square of an arithmetical error term of the Selberg class in short intervals, International Journal of Number Theory Vol. 12, No. 6 (2016) 1675–1701

    · [86] (with X. Cao and Y. Tanigawa)Tong-type identity and the mean square of the error term for an extended Selberg class, Science China Mathematics, Vol.59(2016),  2103–2144

    · [87](with G. Lu anf J. Wu) Shifted convolution of cusp-forms with θ-series, Ramanujan J (2016) 40:115–133

    · [88] (with R. JIa)A weighted divisor problem, Journal of Number Theory 178 (2017) 60–93

    · [89](with L. Toth) On the error term concerning the number of subgroups of the groups Z m × Z n with m,n x, Acta Arithmetica, 183(2018), 285-299.

    · [90] (with L. Toth) On multivariable averages of divisor functions, JNT, 192(2018),  251-269

    · [91] (with P. Song and D. Zhang) Power moments of Hecke eigenvalues for congruence group, Journal of Number Theory 198 (2019) 139–158

    · [92] On a sum involving the Euler function, Journal of Number Theory 211 (2020) 199–219

    · [93](with A. Ivic) ON CERTAIN INTEGRALS INVOLVING THE DIRICHLET DIVISOR PROBLEM, Functiones et Approximatio 62.2 (2020), 247–267 

    · [94](with L. Toth) On the average number of cyclic subgroups of the groups Z n 1 × Z n 2 × Z n 3 with n 1 ,n 2 ,n 3 x, Res.NumberTheory (2020) 6:12

        (4)、短期访问或学术会议 

    · 1.  200111月,京都大学数理研究所:解析数论会议 

    · 2.  200112月, 近畿大学九州工学部 

    · 3.  20025月, 明治学院大学 

    · 4.  20029月, 近畿大学九州工学部 

    · 5.  200210月,京都大学数理研究所:解析数论会议 

    · 6.  20035月, 明治学院大学 

    · 7.  20043月,第3次中日数论会议,西安 

    · 8.  200412月,香港中文大学:ICCM98 

    · 9.  20068月,第4次中日数论会议,威海 

    · 10.  20072月中旬, 名古屋大学多元数理科学研究科 

    · 11.  20084月中旬, 香港大学数学系 

    · 12.  20085月下旬, 中科院晨兴中心,北京 

    · 13.  20088月下旬,第5次中日数论会议:日本大阪 

    · 14.  20089月上旬, 名古屋大学多元数理科学研究科 

    · 15.  20099-12月, 中科院晨兴中心,北京 

    · 16.  20102月中旬, 名古屋大学多元数理科学研究科 

    · 17.  20118月,第6次中日数论会议:上海 

    · 18.  20123月,东京大学 

    · 19.  201210月,第6届全国数论会议:西安 

    · 20.  201211月,第7次中日数论会议:日本福冈 

    · 21.  20138月,香港大学数学系 

    · 22.  20146月,主办解析数论与密码学研讨会,北京 

    · 23.  201410月,中韩数论会议:三亚 

    · 24.  201410月,Workshop on number theory: 西安 

    · 25.  20152月,法国:洛林大学,短期访问。 

    · 26.  20155月, 济南:山东大学,全国第7届数论会议。

    · 27.  201511月,上海:上海交通大学,全国解析数论会议。

    · 28. 2016年6月, 西安:西北大学,数论及其应用研讨会

    · 29. 2016年8月, 西安,西安交通大学数论会议

    · 30. 2016年11月,北京市,组织“2016解析数论与密码学研讨会”

    · 31. 2016年12月,重庆市,第3届川渝数论会议

    · 32. 2017年7月, 西安,解析数论研讨会

    · 33. 2017年9月, 开封:河南大学,数论会议

    · 34. 2017年9月, 杭州:浙江大学, 数论会议

    · 35. 2017年10月,北京,晨兴数学中心讨论班

    · 36. 2017年10月,济南:山东大学,数论会议。

    · 37. 2017年11月,太原:山西大学。

    · 38. 2018年8月,延安,数论会议。

    · 39. 2018年10月,上海大学,数论会议。

    · 40. 2018年10月,澳门科技大学,访问。

    · 41. 2018年10月,芜湖:安徽师范大学,访问。

    · 42. 2018年12月,临沂大学,访问。

    · 43. 2018年12月,成都:四川大学,数论会议。

    · 44. 2019年1月,厦门大学,数论会议。

    · 45. 2019年1月,杭州:浙江大学,访问。

    · 46. 2019年3月,南京师范大学,访问。

    · 47. 2019年4月,重庆:西南大学,访问。

    · 48. 2019年5月,巴彦淖尔:河套学院,数论会议。

    · 49. 2019年6月,宜昌:三峡大学,访问。

    · 50. 2019年6月,烟台大学,访问。

    · 51. 2019年6月,广州:华南师范大学,访问。

    · 52. 2019年7月,深圳:深圳大学,访问。

    · 53. 2019年7月,南昌:南昌大学,访问。

    · 54. 2019年8月,天津大学,数论会议。

    · 55. 2019年8月,哈尔滨工业大学,数论会议。

    · 56. 2019年8月,西藏大学,数论会议。

    · 57. 2019年9月,陕西师范大学,访问。

    · 58. 2019年9月,西北大学,访问。

    · 59. 2019年11月,北京:组织“2019解析数论研讨会”。

    · 60. 2019年12月,重庆: 西南大学,数论会议。

    · 61. 2020年1月,杭州:浙江大学,访问。